This kind of probelm is most likely caused by bad capacitor of your monitors power circuit.

Open up your monitor and see if all the capacitors of the power circuit are OK. OK capacitor is flat on the top.

If you take this guy's advice, DO NOT TOUCH ANYTHING INSIDE THE MONITOR while you're looking. Certain sections of CRTs use very high voltages (tens of kilovolts) and will hold a sizable charge for weeks after you've unplugged it.